The invention relates to a fuel injection pump for an internal combustion engine, in particular a diesel engine. A fuel injection pump of the type to which this invention relates has a cylindrical bore, and traveling therein a piston, the lateral surfaces of which are so embodied as to cooperate with openings in the wall of the cylinder. The injection pump further includes a relief bore, access to which is controlled by appropriately configured surfaces of the pump piston and which creates communication between the pressure line leading to the injection valve and a source of reduced pressure, preferably the suction chamber of the pump. It has been found by experience that the pressure in the individual fuel injection lines leading to the injection valves must be reduced in the time period between fuel injection events. The purpose of the pressure reduction is to avoid dribbling at the nozzles and to adapt the nozzles to the hydraulic conditions of the system. Preferably, the pressure in the pressure lines is kept as low as possible in between injection events. It has further been shown in experiments that good results are obtained with injection systems in which the static pressure is maintained constant, i.e., independent of load and engine rpm. A pressure relief of this type is sometimes called an equal pressure relief and efforts have been made for many decades to obtain a usable solution to this problem. For example, it is known to provide equal pressure relief valves which contain a second valve member controlling the passage from the injection nozzle to the pump working chamber which reduces the pressure in the pressure line after the termination of injection to a value which is determined by the force of the closure spring of the supplementary valve. Valves of this type are quite complicated and expensive to make, especially in multi-cylinder pumps, where it is also difficult to adjust all the individual valves to the same value due to unavoidable variations in dimensions. Furthermore, the changing pressures in the pressure lines do not permit maintaining the same static pressure under all operational conditions of the engine. In known injection pumps of the type described, the equal pressure relief is created by a direct connection between the pressure line and the suction space leading to the fuel injection pump. A relief conduit is opened for this purpose by an oblique control edge of the pump piston and permits a pressure decrease in the pressure line to the pressure which obtains in between injection events. In order to diminish or damp the abrupt pressure pulses during such relief operations, the known injection pumps include throttles in the return line for the fuel. A very serious disadvantage of such known injection pumps is that the fuel displaced by the piston from the moment that fuel delivery is terminated until it has reached its top dead center position is displaced through the pressure valve and through the relief line to the suction chamber. This continuing flow has detrimental and uncontrollable effects on the pressure relief of the valve pressure lines and substantially disrupts the effect of the throttle in the return line.